Analysis of environmental issues and economic performance and population density Executive summary The main goal with the report was to analyse the relationship from 16 different countries on how, if any, CO2 emission per capita is getting affected by population density and GDP per capita by using descriptive statistics and regression. The conclusion is that CO2 emission per capita is affected by changes in GDP per capita and that population density has no significant relation to CO2 emission per capita. Introduction Global warming is one of the biggest problems in the international societies today.
The politician keeps discussing how they can find solutions together to decrease the CO2 emissions worldwide. In this report we will try to examine if well-established countries have a higher CO2 emissions and we will examine how population density are affecting emission in our society today. Aim The aim with this report is first to examine the relationship with GDP per capita and CO2 emission and population density and CO2 emission. Then we will examine if high GDP per capita leads to higher CO2 emission per capita and if countries with low population density are polluting more than countries with high population density.
Hypothesis 1. 1 I believe that a country with high GDP are more likely to have a higher CO2 emission per capita since a country with high GDP are more likely to have higher productivity achieved through higher energy use. We will then start with measuring the linear association between these variables. H0: ? 0?? 1 GDP? 0 (Correlation) H1: ? 0=? 1 GDP=0 (No correlation) Hypothesis 1. 2 I believe that a country with high population density are more likely to have a lower CO2 emission per capita since the inhabitants need travel shorter and less often.
We will therefor measure the linear association for CO2 emission per capita and population density. H0: ? 0?? 2 pop. density? 0 (Correlation) H1: ? 0=? 2 pop. density=0 (No correlation) Main hypothesis We want to find out how much linear association the two variables has on CO2 per capita. This can be done with this model: CO2per capita = ? 0+ ? 1 GDP+? 2 pop. density+ ? H0: ? 1 GDP? 0 H1: ? 1 GDP=0 H0: ? 2 pop. density? 0 H1: ? 2 pop. density=0 We can then see how strong the association these two variables are against the dependent variable CO2 emission per capita. Further on we want to test the significance of these variables.
Data and descriptive statistics The data (GDP per capita, CO2 per capita and population density) in this report is a sample of 16 different countries and are downloaded from the International Monetary Fund, US department of Energy and OECD. All the data are ratio scale and are continuous. Some potential problems with the associated data is: * Some countries may have a high productivity achieved by the efficient labour force and not trough higher energy use. Both ways of high productivity leads to higher GDP per capita, its unlikely to achieve it by efficient labour force, but it can occur. Some countries (e. g. Australia) may have low population density although they mainly have big populated cities since they have a large amount of landmass that is not suitable for life. * The different data is not from the same years. CO2 emission per capita is from 2004, population density is from various years and GDP per capita is from 2010. To get an idea of how the dataset looks like we need to use descriptive analysis. Mean: x=xn Median: x=n+12th S. D: sx=x2-nx2n-1 Sample variance: s2=x2-nx2n-1 Range=xh-xl
For Co2 per capita the mean is 9,285 and the median is 9,49, this will suggest that the data is normally distributed and we can see in the graph in the appendix that there are 8 countries on each side of the mean. The skewness is 0,71, since the number is positive it will imply that Co2 emission per capita is slightly skewed to the right. The mean (26226) and median (27407) for GDP per capita show that this data is normally distributed as well. We can also here see that there are 8 countries on both side of the mean. The skewness for GDP per capita is close to zero (0,08) and therefor the distribution is close to symmetric.
For population density we have 10 countries underneath the mean. This will imply that the data is not perfectly normally distributed. We can also see that mean (151) and the median (118) differs a bit too much too be normally distributed. Since the mean is higher than the media it suggest that the mean is affected by the high extreme values in the distribution like South Korea. The skewness for population density is 0,94, this show that the distribution is skewed to the right. It is important to remember that the data sample is less than 30 and therefor it makes it difficult to determine if the data is normally distributed or not.
In all the 3 different data’s we see that the range is high, this is due extreme values on both sides of the mean (countries in totally different stages when it comes to wealth, industry, population, size and general development). The high spread within the distribution will therefor lead to and high S. D, it’s also important to notice that the sample is relative small and will not give a totally correct picture. Correlation First we will start with to calculate the Pearson correlation coefficient to measure the linear association between the two variables in hypothesis 1. 1 and 1. 2.
After that we will test the significant of the correlation coefficient. The reason we will use the Pearson correlation coefficient instead of Spearman correlation coefficient is that the data are continuous and in ratio scale. sx=x2-nx2n-1 sy=y2-ny2n-1 sxy=i=1n(xi-x)(yi-y)n-1 rxy= sxysxsy t=r1-r2n-2~tn-2 For the calculation see table 1 and 2 in the appendix. The table and the graph 1. 1 show that there is a strong relationship between Co2 emission per capita and GDP (0,7319). In graph 1,2 and the table we see that Co2 and population density have a weak negative correlation (-0,3118).
Further on we will need to use a t-test in order to determine the significant of the correlation coefficient and to find out if we are going to keep or reject our hypothesis 1. 1 and 1. 2. critical value of t: t(n-2,? 2)=t(14,0. 25)=±2,145 (with 95% confidence interval) The t value in the table shows that there is a significant relationship between Co2 emission per capita and GDP since 2,145<4,0186. Therefor we will keep the H0 in our hypothesis 1. 1. The t value for Co2 emission per capita and population density shows that there is no significant relationship -2,145<-1,2281<2,145.
We will therefore need to reject H0 in favour of H1 in hypothesis 1. 2. Multivariate regression We now want to use multivariate regression to test the main hypothesis. In most cases there are unlikely there are only one explanatory factor affecting a dependent variable. We will therefor use multivariate regression to test if the two different explanatory variables (pop. density and GDP per capita) are affecting the dependent variable CO2 emission per capita. From the table we get the regression line: CO2per capita = 4,49432+ 0,0002207 GDP-0,0095956 pop. density+ ?
The coefficient of multiple determination (R square) is 0,59879; normally this would mean that 59,87% of the changes can be explained. However since we are using a sample, have only a few observation and more than one explanatory factor, adjusted R square will give us a more correct and conservative picture. When you add more variables to regression analysis Adjusted R square will only increase if that new variable increases the predictive power of the equation. The adjusted R square shows us that 53,706% of the changes in CO2 emission per capita can be explained by GDP per capita and population density.
Significance F tells us that there are only 0,26% chance that the output was obtain by random chance. If we look at residuals in the graph over (the difference between the actual value of the dependent value and the predicted dependent value) compared to the predicted value, we can see that there are no certain pattern and that there are cantered around zero. See the appendix for the residual output. By using the F-test we can test if the overall model is significant, we will use 95% confidence interval. The critical f-value is 3,806. Since F value (9,70089) is larger than the critical f-value the model is useful.
Since we now know that the overall model is useful we will test the main hypothesis to see if both variables contribute to the model. critical value of t: t(n-2,? 2)=t(13,0. 25)=±2,160 (with 95% confidence interval) The t-value for GDP per capita is 4,03122, since 4,03122<2,160 we will keep H0: ? 1 GDP? 0. This shows us that GDP per capita is contributing to the model and are affecting CO2 emission per capita. The t-value for population density is -1,43036, since -2,160<-1,43036<2,160 we will reject H0 in favour of H1: ? 2 pop. ensity=0, which means that population density is not contributing to the model. Discussion in wider social, economic and political context The results in this report shows that countries with higher GDP per capita are polluting more CO2 per capita. The reason for this is that countries with high GDP per capita are achieving this through higher energy use. This means that countries with high wealth have more industry and are consuming more goods and services. Examples of higher consumption can be cars, travels, heating and lightning. So the result of higher consumption is higher CO2 emission.
A problem is that the wealth in the world is not divided equally between countries or even within the different countries; this implies that CO2 emission is not equally distributed. The Kyoto accord is an international treaty whereby countries agree to reduce their amount of green house gases (CO2 is the most important). The treaty opens for countries to buy credits if it’s cheaper to reduce the CO2 emission in another country. This can create a moral problem since the wealthy countries can “buy” themselves out of the world-polluting problem. Conclusion
The report is using a sample of 16 observation/countries to show that GDP per capita is correlating with CO2 emission per capita and that a higher GDP per capita leads to higher CO2 emission per capita. This proves that countries with high GDP are more likely to achieve higher productivity through higher energy use. The report also shows that population density has no significant relationship with CO2 emission per capita. We can from all the different observations see that there is a very large spread between the wealthy and not wealthy countries.
The main suggestion from this report is to investigation further on how you can increase energy efficiency in a competitive economic world. References * GDP per capita – Gross domestic product per capita in US dollars, 2010; Source International Monetary Fund. http://www. imf. org/external/pubs/ft/weo/2012/02/weodata/ (assessed March 2012) * Population density – number of inhabitants per square kilometre, Source: OECD Various years. United Nations. * Carbon Dioxide Emissions in 2004 – carbon dioxide emissions per capita (tons/capita) 2004, Source: US Department of Energy Appendix
